The total amount of ₹ 14,500 with simple interest in 6 years is ₹ 21,460, find out the Rate of interest per annum?

Options

A. `4%`
B. `10%`
C. `6%`
D. `8%`

Answer

To find the rate of interest per annum, we can use the formula for simple interest and the information given in the question.

### Step 1: Identify the given values
- Principal (P) = ₹ 14,500
- Total Amount (A) = ₹ 21,460
- Time (T) = 6 years

### Step 2: Calculate the Simple Interest (SI)
The formula for the total amount with simple interest is:
\[ A = P + SI \]

From this, we can rearrange to find the Simple Interest:
\[ SI = A - P \]

Substituting the values:
\[ SI = 21,460 - 14,500 \]
\[ SI = 6,960 \]

### Step 3: Use the Simple Interest formula to find the Rate of Interest (R)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]

We can rearrange this formula to find the Rate of Interest (R):
\[ R = \frac{SI \times 100}{P \times T} \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ R = \frac{6,960 \times 100}{14,500 \times 6} \]

### Step 5: Calculate the denominator
First, calculate \( 14,500 \times 6 \):
\[ 14,500 \times 6 = 87,000 \]

### Step 6: Substitute the denominator back into the formula
Now substituting back:
\[ R = \frac{6,960 \times 100}{87,000} \]

### Step 7: Calculate the numerator
Calculate \( 6,960 \times 100 \):
\[ 6,960 \times 100 = 696,000 \]

### Step 8: Final calculation for R
Now, calculate:
\[ R = \frac{696,000}{87,000} \]

### Step 9: Perform the division
Calculating the division:
\[ R = 8 \]

### Conclusion
Thus, the Rate of Interest per annum is **8%**.

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